Subgroups — C₅×#69805 #14294895

Order 1920.

544 conjugacy classes of subgroups.

The subgroup lattice has 180 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×C₅×#97	C₂	1	1	yes	maximal, characteristic
2	C₄²×C₅×Dic₃	C₂	1	1	yes	maximal, characteristic
3	C₂×C₅×#803	C₂	1	1	yes	maximal, characteristic
4	C₅×#4550	C₂	1	4	yes	maximal
5	C₅×#1745	—	3	1	no	maximal, Hall
6	C₂²×C₃×C₅×C₈	C₂²	1	2	yes	—
7	C₂×C₃×C₄²×C₅	C₂²	1	1	yes	characteristic
8	C₂×C₄×C₅×Dic₃	C₄	1	4	yes	—
9	C₂×C₄×C₅×Dic₃	C₂²	1	2	yes	—
10	C₂²×C₅×C₃⋊C₈	C₂²	1	2	yes	—
11	C₃×C₅×#97	C₄	1	4	yes	complemented
12	C₅×#803	C₄	1	4	yes	complemented
13	#69805	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
14	C₂×C₅×#97	—	3	1	no	—
15	C₂×C₅×#97	D₃	1	1	yes	characteristic
16	C₄³×C₅	—	3	1	no	—
17	C₅×#336	—	3	4	no	—
18	C₂²×C₃×C₄×C₅	C₂×C₄	1	2	yes	—
19	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
20	C₂²×C₅×Dic₃	C₂×C₄	1	4	yes	—
21	C₂×C₃×C₅×C₈	—	2	4	no	—
22	C₂×C₃×C₅×C₈	C₂×C₄	1	4	yes	—
23	C₃×C₄²×C₅	C₂×C₄	1	2	yes	—
24	C₃×C₄²×C₅	C₂×C₄	1	2	yes	—
25	C₄×C₅×Dic₃	—	2	4	no	—
26	C₄×C₅×Dic₃	—	2	8	no	—
27	C₂×C₅×C₃⋊C₈	—	2	4	no	—
28	C₂×C₅×C₃⋊C₈	C₂×C₄	1	4	yes	—
29	C₂×C₃×#97	C₂×C₅	1	1	yes	characteristic
30	C₄²×Dic₃	C₂×C₅	1	1	yes	characteristic
31	C₂×#803	C₂×C₅	1	1	yes	characteristic
32	#4550	C₂×C₅	1	4	yes	—
33	C₂²×C₅×C₈	—	3	2	no	—
34	C₂²×C₅×C₈	C₂×D₃	1	2	yes	—
35	C₂×C₄²×C₅	—	3	4	no	—
36	C₂×C₄²×C₅	—	3	2	no	—
37	C₂×C₄²×C₅	C₂×D₃	1	1	yes	characteristic
38	C₅×#97	—	3	4	no	—
39	C₅×#97	Dic₃	1	4	yes	complemented
40	#1745	—	3	1	no	Sylow
41	C₂³×C₃×C₅	C₂²×C₄	1	1	yes	characteristic
42	C₂×C₃×C₄×C₅	—	2	4	no	—
43	C₂×C₃×C₄×C₅	C₄²	1	4	yes	—
44	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
45	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
46	C₂×C₃×C₄×C₅	#41	1	4	yes	—
47	C₂×C₅×Dic₃	—	2	4	no	—
48	C₂×C₅×Dic₃	—	2	4	no	—
49	C₂×C₅×Dic₃	M₁₆	1	8	yes	—
50	C₃×C₅×C₈	—	2	4	no	—
51	C₅×C₃⋊C₈	—	2	4	no	—
52	C₂²×C₃×C₈	C₂²×C₅	1	2	yes	—
53	C₂×C₃×C₄²	C₂²×C₅	1	1	yes	characteristic
54	C₂×C₄×Dic₃	C₄×C₅	1	4	yes	—
55	C₂×C₄×Dic₃	C₂²×C₅	1	2	yes	—
56	C₂²×C₃⋊C₈	C₂²×C₅	1	2	yes	—
57	C₃×#97	C₄×C₅	1	4	yes	complemented
58	#803	C₄×C₅	1	4	yes	complemented
59	C₂²×C₄×C₅	—	3	4	no	—
60	C₂²×C₄×C₅	C₄×D₃	1	2	yes	—
61	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
62	C₂×C₅×C₈	—	2	4	no	—
63	C₂×C₅×C₈	—	3	4	no	—
64	C₂×C₅×C₈	—	6	4	no	—
65	C₂×C₅×C₈	C₂×Dic₃	1	4	yes	—
66	C₄²×C₅	—	6	8	no	—
67	C₄²×C₅	—	6	4	no	—
68	C₄²×C₅	C₄×D₃	1	2	yes	—
69	C₄²×C₅	C₂×Dic₃	1	2	yes	—
70	C₂×#97	—	3	1	no	—
71	C₂×#97	C₅×D₃	1	1	yes	characteristic
72	C₄³	—	3	1	no	—
73	#336	—	3	4	no	—
74	C₂²×C₃×C₅	C₂×C₄²	1	1	yes	characteristic
75	C₂²×C₃×C₅	#117	1	2	yes	—
76	C₂²×C₃×C₅	C₂×M₁₆	1	4	yes	—
77	C₃×C₄×C₅	—	2	4	no	—
78	C₃×C₄×C₅	#117	1	2	yes	—
79	C₃×C₄×C₅	#117	1	2	yes	—
80	C₅×Dic₃	—	2	8	no	—
81	C₂²×C₃×C₄	C₂×C₄×C₅	1	2	yes	—
82	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
83	C₂²×Dic₃	C₂×C₄×C₅	1	4	yes	—
84	C₂×C₃×C₈	—	2	4	no	—
85	C₂×C₃×C₈	C₂×C₄×C₅	1	4	yes	—
86	C₃×C₄²	C₂×C₄×C₅	1	2	yes	—
87	C₃×C₄²	C₂×C₄×C₅	1	2	yes	—
88	C₄×Dic₃	—	2	4	no	—
89	C₄×Dic₃	—	2	8	no	—
90	C₂×C₃⋊C₈	—	2	4	no	—
91	C₂×C₃⋊C₈	C₂×C₄×C₅	1	4	yes	—
92	C₂³×C₅	C₂×C₄×D₃	1	1	yes	characteristic
93	C₂×C₄×C₅	—	2	4	no	—
94	C₂×C₄×C₅	—	3	8	no	—
95	C₂×C₄×C₅	—	6	4	no	—
96	C₂×C₄×C₅	—	6	4	no	—
97	C₂×C₄×C₅	C₄×Dic₃	1	4	yes	—
98	C₂×C₄×C₅	C₂×C₄×D₃	1	1	yes	characteristic
99	C₂×C₄×C₅	#235	1	4	yes	—
100	C₂×C₄×C₅	C₂²×Dic₃	1	1	yes	characteristic
101	C₅×C₈	—	2	4	no	—
102	C₅×C₈	—	6	4	no	—
103	C₂²×C₈	—	3	2	no	—
104	C₂²×C₈	C₂×C₅×D₃	1	2	yes	—
105	C₂×C₄²	—	3	4	no	—
106	C₂×C₄²	—	3	2	no	—
107	C₂×C₄²	C₂×C₅×D₃	1	1	yes	characteristic
108	#97	—	3	4	no	—
109	#97	C₅×Dic₃	1	4	yes	complemented
110	C₂×C₃×C₅	#376	1	1	yes	characteristic
111	C₂×C₃×C₅	C₄×M₁₆	1	2	yes	—
112	C₂×C₃×C₅	#432	1	4	yes	—
113	C₂³×C₃	C₂²×C₄×C₅	1	1	yes	characteristic
114	C₂×C₃×C₄	—	2	4	no	—
115	C₂×C₃×C₄	C₄²×C₅	1	4	yes	—
116	C₂×C₃×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
117	C₂×C₃×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
118	C₂×C₃×C₄	C₅×#41	1	4	yes	—
119	C₂×Dic₃	—	2	4	no	—
120	C₂×Dic₃	—	2	4	no	—
121	C₂×Dic₃	C₅×M₁₆	1	8	yes	—
122	C₃×C₈	—	2	4	no	—
123	C₃⋊C₈	—	2	4	no	—
124	C₂²×C₅	#872	1	2	yes	—
125	C₂²×C₅	D₃×M₁₆	1	4	yes	—
126	C₂²×C₅	C₂×C₄×Dic₃	1	1	yes	characteristic
127	C₄×C₅	—	2	4	no	—
128	C₄×C₅	—	6	8	no	—
129	C₄×C₅	#872	1	2	yes	—
130	C₄×C₅	#926	1	2	yes	—
131	C₂²×C₄	—	3	4	no	—
132	C₂²×C₄	C₄×C₅×D₃	1	2	yes	—
133	C₂²×C₄	C₂²×C₅×D₃	1	1	yes	characteristic
134	C₂×C₈	—	2	4	no	—
135	C₂×C₈	—	3	4	no	—
136	C₂×C₈	—	6	4	no	—
137	C₂×C₈	C₂×C₅×Dic₃	1	4	yes	—
138	C₄²	—	6	8	no	—
139	C₄²	—	6	4	no	—
140	C₄²	C₄×C₅×D₃	1	2	yes	—
141	C₄²	C₂×C₅×Dic₃	1	2	yes	—
142	C₃×C₅	#1745	1	1	yes	characteristic, complemented, Hall
143	C₂²×C₃	C₂×C₄²×C₅	1	1	yes	characteristic
144	C₂²×C₃	C₅×#117	1	2	yes	—
145	C₂²×C₃	C₂×C₅×M₁₆	1	4	yes	—
146	C₃×C₄	—	2	4	no	—
147	C₃×C₄	C₅×#117	1	2	yes	—
148	C₃×C₄	C₅×#117	1	2	yes	—
149	Dic₃	—	2	8	no	—
150	C₂×C₅	#4705	1	4	yes	—
151	C₂×C₅	#4932	1	1	yes	characteristic
152	C₂×C₅	Dic₃×M₁₆	1	2	yes	—
153	C₂³	C₂×C₄×C₅×D₃	1	1	yes	characteristic
154	C₂×C₄	—	2	4	no	—
155	C₂×C₄	—	3	8	no	—
156	C₂×C₄	—	6	4	no	—
157	C₂×C₄	—	6	4	no	—
158	C₂×C₄	C₄×C₅×Dic₃	1	4	yes	—
159	C₂×C₄	C₂×C₄×C₅×D₃	1	1	yes	characteristic
160	C₂×C₄	C₅×#235	1	4	yes	—
161	C₂×C₄	C₂²×C₅×Dic₃	1	1	yes	characteristic
162	C₈	—	2	4	no	—
163	C₈	—	6	4	no	—
164	C₂×C₃	C₅×#376	1	1	yes	characteristic
165	C₂×C₃	C₄×C₅×M₁₆	1	2	yes	—
166	C₂×C₃	C₅×#432	1	4	yes	—
167	C₅	#69805	1	1	yes	characteristic, direct product factor, Sylow
168	C₂²	C₅×#872	1	2	yes	—
169	C₂²	C₅×D₃×M₁₆	1	4	yes	—
170	C₂²	C₂×C₄×C₅×Dic₃	1	1	yes	characteristic
171	C₄	—	2	4	no	—
172	C₄	—	6	8	no	—
173	C₄	C₅×#872	1	2	yes	—
174	C₄	C₅×#926	1	2	yes	—
175	C₃	C₅×#1745	1	1	yes	characteristic, complemented, Sylow
176	C₂	C₅×#4705	1	4	yes	—
177	C₂	C₅×#4932	1	1	yes	characteristic
178	C₂	C₅×Dic₃×M₁₆	1	2	yes	—

	subgroup	G/H
center	C₂²×C₄×C₅	C₂²×D₃
commutator	C₂²×C₃	C₂×C₄²×C₅
Frattini	C₂²×C₄	C₂²×C₅×D₃
Fitting	C₂×C₃×C₅×#97	C₂
socle, prime radical	C₂³×C₃×C₅	C₂²×C₄
cosocle	C₂²×C₃×C₄	C₂³×C₅
hypercenter	C₂×C₅×#97	D₃
hypocenter	C₃	C₅×#1745
LCS	G ▷ C₂²×C₃ ▷ C₃
UCS	C₁ ◁ C₂²×C₄×C₅ ◁ C₂×C₅×#97

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
11. C₃×C₅×#97	C₄	semidirect
12. C₅×#803	C₄	semidirect
13. #69805	C₅	direct (N × H)
39. C₅×#97	Dic₃	semidirect
57. C₃×#97	C₄×C₅	semidirect
58. #803	C₄×C₅	semidirect
109. #97	C₅×Dic₃	semidirect
142. C₃×C₅	#1745	semidirect
167. C₅	#69805	direct (N × H)
175. C₃	C₅×#1745	semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₂×C₃×C₅×#97	2
C₄²×C₅×Dic₃	2
C₂×C₅×#803	2
C₅×#4550	2
C₅×#1745	3
#69805	5

Subgroups — C5×#69805 #14294895

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#69805 #14294895